The way it typically works is this: Businesses are looking to solve a problem. It could be solved with software, or it could be solved with process improvements. Or it could be solved by a little of both.
It may take 6 months or it may take three weeks.
Despite your credentials, you still seem a little inexperienced. Maybe not in software, but definitely in the business of software. Inexperienced developers tend to think too big in terms of scope. Again, I say inexperienced in the business of software, not necessarily as a developer. There is a difference.
Therefore, your best bet is to start off small. Look for businesses that just need a small change done. This will get you to the point where you're talking to real customers and finding out what they really need. In most cases, many businesses are going to just use pre-built software because it's cheaper and has been tried and tested in many different businesses and environments. Custom-built software is expensive, and most businesses who build custom software will either do it in-house or with experienced contractors. What's more, custom software is a long-term commitment with support contracts and SLA's and things that may arguably be difficult for a single sole proprietor to support.
So, instead of approaching these businesses with a 6 month scope of work in an offer letter before even finding out what they're about, word it so that it sounds like you want to help them solve a problem. If you approach them with the idea that you're going to spend six months working on enterprise database software when all they really need is a simple solution to manage a few documents, they're immediately going to think that you're not really going to listen to their needs. The last thing any business wants to deal with is a contractor who doesn't listen to them.
Years ago, I worked for a company that needed a website built, and we hired a few different contractors because they all said they'd build the HTML to standard but ended up using tables (for non-technical readers, that's an outdated methodology). We finally found a contractor who would listen to what we needed, and that person got our repeat business.